State Rolle’s theorem.
Question:

State Rolle’s theorem.

Solution:

Let $f$ be a real valued function defined on the closed interval $[a, b]$ such that (i) it is continuous on the closed interval $[a, b]$,

(ii) it is differentiable on the open interval $(a, b)$, and

(iii) $f(a)=f(b)$

Then, there exists a real number $c \in(a, b)$ such that $f^{\prime}(c)=0$.